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{{Infobox Particle
| bgcolour        =
| name            = Lepton
| image          = [[File:Beta Negative Decay.svg|200px]]
| caption        = Leptons are involved in several processes such as [[beta decay]].
| num_types      = 6 ([[electron]], [[electron neutrino]], [[muon]], [[muon neutrino]], [[tau (particle)|tau]], [[tau neutrino]])
| composition    = [[Elementary particle]]
| statistics      = [[Fermionic]]
| group          =
| generation      = 1st, 2nd, 3rd
| interaction    = [[Electromagnetism]], [[Gravitation]], [[Weak interaction|Weak]]
| particle        =
| antiparticle    = Antilepton ({{SubatomicParticle|Antilepton}})
| theorized      =
| discovered      =
| symbol          = {{SubatomicParticle|Lepton}}
| baryon number  = 0
| mass            =
| decay_time      =
| decay_particle  =
| electric_charge = +1 [[elementary charge|e]], 0 e, −1 e
| color_charge    = No
| spin            = {{Frac|1|2}}
| num_spin_states =
}}
 
A '''lepton''' is an [[elementary particle|elementary]], spin-{{Frac|1|2}} particle that does not undergo strong interactions, but is subject to the [[Pauli exclusion principle]].<ref>
{{cite web
|author=
|title=Lepton (physics)
|url=http://www.britannica.com/EBchecked/topic/336940/lepton
|work=[[Encyclopædia Britannica]]
|year=
|accessdate=2010-09-29
}}</ref> The best known of all leptons is the [[electron]], which governs nearly all of [[chemistry]] as it is found in [[atom]]s and is directly tied to all [[chemical property|chemical properties]]. Two main classes of leptons exist: [[electric charge|charged]] leptons (also known as the ''[[electron]]-like'' leptons), and neutral leptons (better known as [[neutrino]]s). Charged leptons can combine with other particles to form various [[composite particle]]s such as [[atom]]s and [[positronium]], while neutrinos rarely interact with anything, and are consequently rarely observed.
 
There are six types of leptons, known as ''[[flavour (particle physics)|flavours]]'', forming three ''[[Generation (particle physics)|generations]]''.<ref name="HyperphysicsLepton">
{{cite web
|author=R. Nave
|title=Leptons
|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/lepton
|work=[[HyperPhysics]]
  |publisher=[[Georgia State University]], Department of Physics and Astronomy
|year=
|accessdate=2010-09-29
}}</ref>  The first generation is the ''electronic leptons'', comprising the [[electron]] ({{SubatomicParticle|Electron-}}) and [[electron neutrino]] ({{SubatomicParticle|Electron neutrino}}); the second is the ''muonic leptons'', comprising the [[muon]] ({{SubatomicParticle|Muon-}}) and [[muon neutrino]] ({{SubatomicParticle|Muon neutrino}}); and the third is the ''tauonic leptons'', comprising the [[Tau (particle)|tau]] ({{SubatomicParticle|Tau-}}) and the [[tau neutrino]] ({{SubatomicParticle|Tau neutrino}}). Electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons through a process of [[particle decay]]: the transformation from a higher mass state to a lower mass state. Thus electrons are stable and the most common charged lepton in the [[universe]], whereas muons and taus can only be produced in [[high energy physics|high energy]] collisions (such as those involving [[cosmic ray]]s and those carried out in [[particle accelerator]]s).
 
Leptons have various intrinsic properties, including [[electric charge]], [[spin (physics)|spin]], and [[mass]]. Unlike [[quark]]s however, leptons are not subject to the [[strong interaction]], but they are subject to the other three [[fundamental interaction]]s: [[gravitation]], [[electromagnetism]] (excluding neutrinos, which are electrically neutral), and the [[weak interaction]]. For every lepton flavor there is a corresponding type of [[antiparticle]], known as [[antilepton]], that differs from the lepton only in that some of its properties have [[additive inverse|equal magnitude but opposite sign]]. However, according to certain theories, neutrinos may be [[Majorana fermion|their own antiparticle]], but it is not currently known whether this is the case or not.
 
The first charged lepton, the electron, was theorized in the mid-19th century by several scientists<ref name="farrar">
{{cite journal
|author=W.V. Farrar
|year=1969
|title=Richard Laming and the Coal-Gas Industry, with His Views on the Structure of Matter
|journal=[[Annals of Science]]
|volume=25
|issue=3 |pages=243–254
|doi=10.1080/00033796900200141
}}</ref><ref name="arabatzis">
{{cite book
|author=T. Arabatzis
|year=2006
|title=Representing Electrons: A Biographical Approach to Theoretical Entities
|url=http://books.google.com/?id=rZHT-chpLmAC&pg=PA70
|pages=70–74
|publisher=[[University of Chicago Press]]
|isbn=0-226-02421-0
}}</ref><ref name="buchwald1">
{{cite book
|author=J.Z. Buchwald, A. Warwick
|year=2001
|title=Histories of the Electron: The Birth of Microphysics
|url=http://books.google.com/?id=1yqqhlIdCOoC&pg=PA195
|pages=195–203
|publisher=[[MIT Press]]
|isbn=0-262-52424-4
}}</ref> and was discovered in 1897 by [[J. J. Thomson]].<ref name="thomson">
{{cite journal
|author=J.J. Thomson
|year=1897
|title=Cathode Rays
|url=http://web.lemoyne.edu/~GIUNTA/thomson1897.html
|journal=[[Philosophical Magazine]]
|volume=44 |page=293
|doi=10.1080/14786449708621070
|issue=269
}}</ref> The next lepton to be observed was the [[muon]], discovered by [[Carl D. Anderson]] in 1936, but it was erroneously classified as a [[meson]] at the time.<ref>
{{cite journal
|author=S.H. Neddermeyer, C.D. Anderson
|year=1937
|title=Note on the Nature of Cosmic-Ray Particles
|journal=[[Physical Review]]
|volume=51
|issue=10 |pages=884–886
|doi=10.1103/PhysRev.51.884
|bibcode = 1937PhRv...51..884N }}</ref> After investigation, it was realized that the muon did not have the expected properties of a meson, but rather behaved like an electron, only with higher mass. It took until 1947 for the concept of "leptons" as a family of particle to be proposed.<ref name=LAS/> The first neutrino, the electron neutrino, was proposed by [[Wolfgang Pauli]] in 1930 to explain certain characteristics of [[beta decay]].<ref name=LAS/> It was first observed in the [[Cowan–Reines neutrino experiment]] conducted by [[Clyde Cowan]] and [[Frederick Reines]] in 1956.<ref name=LAS>
{{cite journal
|author=
|year=1997
|title=The Reines-Cowan Experiments: Detecting the Poltergeist
|journal=[[Los Alamos Science]]
|volume=25 |issue= |page=3
|url=http://library.lanl.gov/cgi-bin/getfile?25-02.pdf
|accessdate=2010-02-10
}}</ref><ref>
{{cite journal
|author=F. Reines, C.L. Cowan, Jr.
|year=1956
|title=The Neutrino
|journal=[[Nature (journal)|Nature]]
|volume=178
|issue=4531 |page=446
|doi=10.1038/178446a0
|bibcode = 1956Natur.178..446R }}</ref> The muon neutrino was discovered in 1962 by [[Leon M. Lederman]], [[Melvin Schwartz]] and [[Jack Steinberger]],<ref name="slac.stanford.edu">
{{cite journal
|author=G. Danby ''et al.''
|year=1962
|title=Observation of high-energy neutrino reactions and the existence of two kinds of neutrinos
|url=http://www.slac.stanford.edu/spires/find/hep/www?j=PRLTA,9,36
|journal=[[Physical Review Letters]]
|volume=9 |page=36
|doi=10.1103/PhysRevLett.9.36
|bibcode = 1962PhRvL...9...36D
|last2=Gaillard
|first2=J-M.
|last3=Goulianos
|first3=K.
|last4=Lederman
|first4=L.
|last5=Mistry
|first5=N.
|last6=Schwartz
|first6=M.
|last7=Steinberger
|first7=J. }}</ref> and the tau discovered between 1974 and 1977 by [[Martin Lewis Perl]] and his colleagues from the [[Stanford Linear Accelerator Center]] and [[Lawrence Berkeley National Laboratory]].<ref>
{{cite journal
|author=M.L. Perl ''et al.''
|title=Evidence for Anomalous Lepton Production in {{SubatomicParticle|Positron}}{{SubatomicParticle|Electron}} Annihilation
|journal=[[Physical Review Letters]]
|volume=35 |issue=22 |page=1489
|year=1975
|doi=10.1103/PhysRevLett.35.1489
|bibcode=1975PhRvL..35.1489P
|last2=Abrams
|first2=G.
|last3=Boyarski
|first3=A.
|last4=Breidenbach
|first4=M.
|last5=Briggs
|first5=D.
|last6=Bulos
|first6=F.
|last7=Chinowsky
|first7=W.
|last8=Dakin
|first8=J.
|last9=Feldman
|first9=G.
}}</ref> The [[tau neutrino]] remained elusive until July 2000, when the [[DONUT|DONUT collaboration]] from [[Fermilab]] announced its discovery.<ref name=tauonpress>
{{cite press
|author=
|date=20 July 2000
|title=Physicists Find First Direct Evidence for Tau Neutrino at Fermilab
|url=http://www.fnal.gov/pub/presspass/press_releases/donut.html
|publisher=[[Fermilab]]
}}</ref><ref name=tauonpaper>
{{cite journal
|author=K. Kodama ''et al.'' ([[DONUT|DONUT Collaboration]])
|year=2001
|title=Observation of tau neutrino interactions
|journal=[[Physics Letters B]]
|volume=504
|issue=3 |page=218
|doi=10.1016/S0370-2693(01)00307-0
|arxiv = hep-ex/0012035 |bibcode = 2001PhLB..504..218D }}</ref>
 
Leptons are an important part of the [[Standard Model]]. Electrons are one of the components of [[atom]]s, alongside [[proton]]s and [[neutron]]s. [[Exotic atom]]s with muons and taus instead of electrons can also be synthesized, as well as lepton–antilepton particles such as [[positronium]].
 
==Etymology==
The name ''lepton'' comes from the [[Greek language|Greek]] "λεπτόν" (''lepton''), neuter of "λεπτός" (''leptos''), "fine, small, thin"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dlepto%2Fs λεπτός], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref> and the earliest attested form of the word is the [[Mycenaean Greek]] ''re-po-to'', written in [[Linear B]] syllabic script.<ref>[http://www.palaeolexicon.com Palaeolexicon], Word study tool of ancient languages</ref>  ''Lepton'' was first used by physicist [[Léon Rosenfeld]] in 1948:<ref>L. Rosenfeld (1948)</ref>
<blockquote>Following a suggestion of Prof. [[C. Møller]], I adopt — as a pendant to "nucleon" — the denomination "lepton" (from λεπτός, small, thin, delicate) to denote a particle of small mass.</blockquote>
 
The etymology incorrectly implies that all the leptons are of small mass. When Rosenfeld named them, the only known leptons were electrons and muons, which are in fact of small mass — the mass of an electron ({{val|0.511|ul=MeV/c2}})<ref name="Electron">C. Amsler ''et al''. (2008): [http://pdg.lbl.gov/2008/listings/s003.pdf Particle listings – {{SubatomicParticle|Electron-}}]</ref> and the mass of a muon (with a value of {{val|105.7|u=MeV/c2}})<ref name="Muon">C. Amsler ''et al''. (2008): [http://pdg.lbl.gov/2008/listings/s004.pdf Particle listings – {{SubatomicParticle|Muon-}}]</ref> are fractions of the mass of the "heavy" proton ({{val|938.3|u=MeV/c2}}).<ref name="Proton">C. Amsler ''et al''. (2008): [http://pdg.lbl.gov/2008/listings/s016.pdf Particle listings – {{SubatomicParticle|Proton+}}]</ref> However, the mass of the tau (discovered in the mid 1970s) ({{val|1777|u=MeV/c2}})<ref name="Tauon">C. Amsler ''et al''. (2008): [http://pdg.lbl.gov/2008/listings/s035.pdf Particle listings – {{SubatomicParticle|Tau-}}]</ref> is nearly twice that of the proton, and about 3,500 times that of the electron.
 
== History ==
{{See also|Electron#Discovery|Muon#History|Tau (particle)#History}}
[[Image:Muon-Electron-Decay.svg|left|200px|thumb|A muon transmutes into a [[muon neutrino]] by emitting a [[W boson|{{SubatomicParticle|W boson-}} boson]]. The {{SubatomicParticle|W boson-}} boson subsequently decays into an [[electron]] and an [[electron antineutrino]].]]
{| class="wikitable"  style="float:right; font-size:90%; margin:.5em 0 .5em 1em;"
|+Lepton nomenclature
|-
!Particle name !! Antiparticle name
|-
|Electron || Antielectron<br>Positron
|-
|Electron neutrino || Electron antineutrino
|-
|Muon<br>Mu lepton<br>Mu || Antimuon<br>Antimu lepton<br>Antimu
|-
|Muon neutrino<br>Muonic neutrino<br>Mu neutrino || Muon antineutrino<br>Muonic antineutrino<br>Mu antineutrino
|-
|Tau<br>Tau lepton<br>Tauon || Antitau<br>Antitau lepton<br>Antitauon
|-
|Tau neutrino<br>Tauonic neutrino || Tau antineutrino<br>Tauonic antineutrino
|}
 
The first lepton identified was the electron, discovered by [[J.J. Thomson]] and his team of British physicists in 1897.<ref>S. Weinberg (2003)</ref><ref>R. Wilson (1997)</ref> Then in 1930 [[Wolfgang Pauli]] postulated the [[electron neutrino]] to preserve [[conservation of energy]], [[conservation of momentum]], and [[conservation of angular momentum]] in [[beta decay]].<ref>K. Riesselmann (2007)</ref> Pauli theorized that an undetected particle was carrying away the difference between the [[energy]], [[momentum]], and [[angular momentum]] of the initial and observed final particles. The electron neutrino was simply called the neutrino, as it was not yet known that neutrinos came in different flavours (or different "generations").
 
Nearly 40 years after the discovery of the electron, the [[muon]] was discovered by [[Carl D. Anderson]] in 1936.  Due to its mass, it was initially categorized as a [[meson]] rather than a lepton.<ref>S.H. Neddermeyer, C.D. Anderson (1937)</ref>  It later became clear that the muon was much more similar to the electron than to mesons, as muons do not undergo the [[strong interaction]], and thus the muon was reclassified: electrons, muons, and the (electron) neutrino were grouped into a new group of particles – the leptons. In 1962 [[Leon M. Lederman]], [[Melvin Schwartz]] and [[Jack Steinberger]] showed that more than one type of neutrino exists by first detecting interactions of the [[muon]] neutrino, which earned them the [[Nobel Prize in Physics|1988 Nobel Prize]], although by then the different flavours of neutrino had already been theorized.<ref>I.V. Anicin (2005)</ref>
 
The [[tau (particle)|tau]] was first detected in a series of experiments between 1974 and 1977 by [[Martin Lewis Perl]] with his colleagues at the [[SLAC]] [[Lawrence Berkeley National Laboratory|LBL group]].<ref>M.L. Perl et al. (1975)</ref> Like the electron and the muon, it too was expected to have an associated neutrino. The first evidence for tau neutrinos came from the observation of "missing" energy and momentum in tau decay, analogous to the "missing" energy and momentum in beta decay leading to the discovery of the electron neutrino. The first detection of tau neutrino interactions was announced in 2000 by the [[DONUT]] collaboration at [[Fermilab]], making it the latest particle of the [[Standard Model]] to have been directly observed,<ref name="obs">K. Kodama (2001)</ref> apart from the [[Higgs boson]], which probably has been discovered in 2012.
 
Although all present data is consistent with three generations of leptons, some particle physicists are searching for a fourth generation. The current lower limit on the mass of such a fourth charged lepton is {{val|100.8|ul=GeV/c2}},<ref>C. Amsler ''et al''. (2008) [http://pdg.lbl.gov/2008/listings/s025.pdf Heavy Charged Leptons Searches]</ref> while its associated neutrino would have a mass of at least {{val|45.0|ul=GeV/c2}}.<ref>C. Amsler ''et  al''. (2008) [http://pdg.lbl.gov/2008/listings/s077.pdf Searches for Heavy Neutral Leptons]</ref>
 
==Properties==
 
=== Spin and chirality ===
[[Image:Right left helicity.svg|thumb|200px|right|Left-handed and right-handed helicities]]
 
Leptons are [[spin (physics)|spin]]-{{frac|1|2}} particles. The [[spin-statistics theorem]] thus implies that they are [[fermion]]s and thus that they are subject to the [[Pauli exclusion principle]]; no two leptons of the same species can be in exactly the same state at the same time. Furthermore, it means that a lepton can have only two possible spin states, namely up or down.
A closely related property is [[chirality (physics)|chirality]], which in turn is closely related to a more easily visualized property called [[helicity (particle physics)|helicity]]. The helicity of a particle is the direction of its spin relative to its [[momentum]]; particles with spin in the same direction as their momentum are called ''right-handed'' and otherwise they are called ''left-handed''. When a particle is mass-less, the direction of its momentum relative to its spin is frame independent, while for massive particles it is possible to 'overtake' the particle by a [[Lorentz transformation]] flipping the helicity. Chirality is a technical property (defined through the transformation behaviour under the [[Poincaré group]]) that agrees with helicity for (approximately) massless particles and is still well defined for massive particles.
 
In many [[quantum field theories]]—such as [[quantum electrodynamics]] and [[quantum chromodynamics]]—left and right-handed fermions are identical. However in the Standard Model left-handed and right-handed fermions are treated asymmetrically. Only left-handed fermions participate in the [[weak interaction]], while there are no right-handed neutrinos. This is an example of [[parity violation]]. In the literature left-handed fields are often denoted by a capital ''L'' subscript (e.g. {{SubatomicParticle|electron}}<sub>L</sub>) and right-handed fields are denoted by a capital ''R'' subscript.
{{clr}}
 
=== Electromagnetic interaction ===
[[Image:Lepton-interaction-vertex-eeg.svg|thumb|portrait|right|Lepton-photon interaction]]
One of the most prominent properties of leptons is their [[electric charge]], ''Q''. The electric charge determines the strength of their electromagnetic interactions. It determines the strength of the [[electric field]] generated by the particle (see [[Coulomb's law]]) and how strongly the particle reacts to an external electric or magnetic field (see [[Lorentz force]]). Each generation contains one lepton with ''Q''&nbsp;=&nbsp;−1 (conventionally the charge of a particle is expressed in units of the [[elementary charge]]) and one lepton with zero electric charge. The lepton with electric charge is commonly simply referred to as a 'charged positive lepton' while the neutral lepton is called a neutrino. For example the first generation consists of the electron {{SubatomicParticle|electron}} with a negative electric charge and the electrically neutral electron neutrino {{SubatomicParticle|electron neutrino}}.
 
In the language of quantum field theory the electromagnetic interaction of the charged leptons is expressed by the fact that the particles interact with the quantum of the electromagnetic field, the [[photon]]. The [[Feynman diagram]] of the electron-photon interaction is shown on the right.
 
Because leptons possess an intrinsic rotation in the form of their spin, charged leptons generate a magnetic field. The size of their [[magnetic dipole moment]] ''μ'' is given by,
:<math>\mu = g \frac{ Q e \hbar}{4 m}, </math>
where ''m'' is the mass of the lepton and ''g'' is the so-called [[g-factor (physics)|g-factor]] for the lepton.  First order approximation quantum mechanics predicts that the g-factor is 2 for all leptons. However, higher order quantum effects caused by loops in Feynman diagrams introduce corrections to this value. These corrections, referred to as the [[anomalous magnetic dipole moment]], are very sensitive to the details of a quantum field theory model and thus provide the opportunity for precision tests of the standard model. The theoretical and measured values for the electron anomalous magnetic dipole moment are within agreement within eight significant figures.<ref>M.E. Peskin, D.V. Schroeder (1995), p. 197</ref>
 
=== Weak Interaction ===
{|  style="float:right; margin: 0em 0em 1em 1em "
|-
|
{|class=wikitable style="font-size:90%;"
|[[Image:Lepton-interaction-vertex-evW.svg|frameless|upright=.7]]
|[[Image:Lepton-interaction-vertex-pvW.svg|frameless|upright=.7]]
|[[Image:Lepton-interaction-vertex-eeZ.svg|frameless|upright=.7]]
|-
|colspan=3|The weak interactions of the first generation leptons.
|}
|}
In the Standard Model the left-handed charged lepton and the left-handed neutrino are arranged in [[Doublet (physics)|doublet]] {{nowrap|({{SubatomicParticle|electron neutrino}}<sub>L</sub>, {{SubatomicParticle|electron}}<sub>L</sub>)}} that transforms in the [[spinor]] representation (''T''&nbsp;=&nbsp;{{frac|1|2}}) of the [[weak isospin]] [[SU(2)]] gauge symmetry. This means that these particles are eigenstates of the isospin projection ''T''<sub>3</sub> with eigenvalues {{frac|1|2}} and −{{frac|1|2}} respectively. In the meantime, the right-handed charged lepton transforms as a weak isospin scalar (''T''&nbsp;=&nbsp;0) and thus does not participate in the weak interaction, while there is no right-handed neutrino at all.
 
The [[Higgs mechanism]] recombines the gauge fields of the weak isospin SU(2) and the [[weak hypercharge]] U(1) symmetries to three massive vector bosons ({{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson-}}, {{SubatomicParticle|Z boson0}}) mediating the weak interaction, and one massless vector boson, the photon, responsible for the electromagnetic interaction. The electric charge ''Q'' can be calculated from the isospin projection ''T''<sub>3</sub> and weak hypercharge ''Y''<sub>W</sub> through the [[Gell-Mann–Nishijima formula]],
:''Q'' = ''T''<sub>3</sub> + ''Y''<sub>W</sub>/2
To recover the observed electric charges for all particles the left-handed weak isospin doublet {{nowrap|({{SubatomicParticle|electron neutrino}}<sub>L</sub>, {{SubatomicParticle|electron}}<sub>L</sub>)}} must thus have ''Y''<sub>W</sub>&nbsp;=&nbsp;−1, while the right-handed isospin scalar e{{su|p=−|b=R}} must have ''Y''<sub>W</sub>&nbsp;=&nbsp;−2. The interaction of the leptons with the massive weak interaction vector bosons is shown in the figure on the left.
 
=== Mass ===
In the [[Standard Model]] each lepton starts out with no intrinsic mass. The charged leptons (i.e. the electron, muon, and tau) obtain an effective mass through interaction with the [[Higgs field]], but the neutrinos remain massless. For technical reasons the masslessness of the neutrinos implies that there is no mixing of the different generations of charged leptons as [[CKM matrix|there is for quarks]]. This is in close agreement with current experimental observations.<ref>M.E. Peskin, D.V. Schroeder (1995), p. 27</ref>
 
It is however known from experiment – most prominently from observed [[neutrino oscillation]]s<ref>Y. Fukuda ''et al''. (1998)</ref> – that neutrinos do in fact have some very small mass, probably less than {{val|2|ul=eV/c2}}.<ref name="Neutrino"/> This implies that there are physics [[beyond the Standard Model]]. The currently most favoured extension is the so-called [[seesaw mechanism]], which would explain both why the left-handed neutrinos are so light compared to the corresponding charged leptons, and why we have not yet seen any right-handed neutrinos.
 
=== Leptonic numbers ===
{{Main|Lepton number}}
The members of each generation's [[weak isospin]] [[doublet (physics)|doublet]] are assigned [[lepton number|leptonic numbers]] that are conserved under the Standard Model.<ref name="MartinShaw">B.R. Martin, G. Shaw (1992)</ref> Electrons and electron neutrinos have an ''electronic number'' of ''L''<sub>e</sub>&nbsp;=&nbsp;1, while muons and muon neutrinos have a ''muonic number'' of ''L''<sub>μ</sub>&nbsp;=&nbsp;1, while tau particles and tau neutrinos have a ''tauonic number'' of  ''L''<sub>τ</sub>&nbsp;=&nbsp;1. The antileptons have their respective generation's leptonic numbers of −1.
 
Conservation of the leptonic numbers means that the number of leptons of the same type remains the same, when particles interact. This implies that leptons and antileptons must be created in pairs of a single generation. For example, the following processes are allowed under conservation of leptonic numbers:{{clr}}
[[Image:Lepton isodoublets fixed.png|thumb|right|Each generation forms a [[weak isospin]] [[Doublet (physics)|doublet]].]]
:{{SubatomicParticle|link=yes|Electron}} + {{SubatomicParticle|link=yes|Antielectron}} &rarr; {{SubatomicParticle|link=yes|Photon}} +  {{SubatomicParticle|link=yes|Photon}},
:{{SubatomicParticle|link=yes|Tau}} + {{SubatomicParticle|link=yes|Antitau}} &rarr; {{SubatomicParticle|link=yes|Z boson0}} +  {{SubatomicParticle|link=yes|Z boson0}},
 
but not these:
 
:{{SubatomicParticle|link=yes|Photon}} &rarr; {{SubatomicParticle|link=yes|Electron}} + {{SubatomicParticle|link=yes|Antimuon}},
:{{SubatomicParticle|link=yes|W boson-}} &rarr; {{SubatomicParticle|link=yes|Electron}} + {{SubatomicParticle|link=yes|Tau neutrino}},
:{{SubatomicParticle|link=yes|Z boson0}} &rarr; {{SubatomicParticle|link=yes|Muon}} + {{SubatomicParticle|link=yes|Antitau}}.
 
However, [[neutrino oscillation]]s are known to violate the conservation of the individual leptonic numbers. Such a violation is considered to be smoking gun evidence for [[Beyond the Standard Model|physics beyond the Standard Model]]. A much stronger conservation law is the conservation of the total number of leptons (''L''), conserved even in the case of neutrino oscillations, but even it is still violated by a tiny amount by the [[chiral anomaly]].
 
== Universality ==
 
The coupling of the leptons to [[gauge boson]]s are flavour-independent (i.e., the interactions between leptons and gauge bosons are the same for all leptons).<ref name="MartinShaw"/> This property is called ''lepton universality'' and has been tested in measurements of the tau and muon [[mean lifetime|lifetime]]s and of [[Z boson]] partial [[decay width]]s, particularly at the [[Stanford Linear Collider]] (SLC) and [[Large Electron-Positron Collider]] (LEP) experiments.{{Citation needed|date=November 2008}}
 
The decay rate (''Γ'') of muons through the process {{SubatomicParticle|link=yes|muon-}} → {{SubatomicParticle|link=yes|electron-}} + {{SubatomicParticle|link=yes|electron antineutrino}} + {{SubatomicParticle|link=yes|muon neutrino}} is approximately given by an expression of the form (see [[muon decay]] for more details)<ref name="MartinShaw"/>
 
: <math>\Gamma \left ( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right ) = K_1G_F^2m_\mu^5,</math>
 
where ''K''<sub>1</sub> is some constant, and ''G''<sub>F</sub> is the [[Fermi coupling constant]]. The decay rate of tau particles through the process {{SubatomicParticle|link=yes|tau-}} → {{SubatomicParticle|link=yes|electron-}} + {{SubatomicParticle|link=yes|electron antineutrino}} + {{SubatomicParticle|link=yes|tau neutrino}} is given by an expression of the same form<ref name="MartinShaw"/>
 
: <math>\Gamma \left ( \tau^- \rarr e^- + \bar{\nu_e} +\nu_\tau \right ) = K_2G_F^2m_\tau^5,</math>
 
where ''K''<sub>2</sub> is some constant. Electron–muon universality implies that ''K''<sub>1</sub>&nbsp;=&nbsp;''K''<sub>2</sub>, and thus<ref name="MartinShaw"/>
: <math>\Gamma \left ( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right ) = \Gamma \left ( \tau^- \rarr \mu^- + \bar{\nu_\mu} +\nu_\tau \right ).</math>
 
This explains why the [[branching ratio]]s for the electronic mode (17.85%) and muonic (17.36%) mode of tau decay are equal (within error).<ref name="Tauon"/>
 
Universality also accounts for the ratio of muon and tau lifetimes. The lifetime of a lepton (''τ''<sub>l</sub>) is related to the decay rate by<ref name="MartinShaw"/>
 
: <math>\tau_l=\frac{B \left ( l^- \rarr e^- + \bar{\nu_e} +\nu_l \right )}{\Gamma \left ( l^- \rarr e^- + \bar{\nu_e} +\nu_l \right )},</math>
 
where ''B''(x → y) and ''Γ''(x → y) denotes the branching ratios and the [[decay width|resonance width]] of the process x → y.
 
The ratio of tau and muon lifetime is thus given by<ref name="MartinShaw"/>
: <math>\frac{\tau_\tau}{\tau_\mu} = \frac{B \left ( \tau^- \rarr e^- + \bar{\nu_e} +\nu_\tau \right )}{B \left ( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right )}\left (\frac{m_\mu}{m_\tau}\right )^5.</math>
 
Using the values of the 2008 ''[[Review of Particle Physics]]'' for the branching ratios of muons<ref name="Muon"/> and tau<ref name="Tauon"/>  yields a lifetime ratio of ~{{val|1.29|e=-7}}, comparable to the measured lifetime ratio of ~{{val|1.32|e=-7}}. The difference is due to ''K''<sub>1</sub> and ''K''<sub>2</sub> not actually being constants; they depend on the mass of leptons.
 
== Table of leptons ==
 
{| class="wikitable" style="text-align:center"
|+Properties of leptons
|-
! Particle/Antiparticle Name
! Symbol
! [[Electric charge|Q]] ([[elementary charge|e]])
! [[Spin (physics)|S]]
! L<sub>e</sub>
! L<sub>μ</sub>
! L<sub>τ</sub>
! Mass (MeV/c<sup>2</sup>)
! Lifetime ([[second|s]])
! Common decay
|-
|style="text-align:left"| [[Electron]] / [[Positron]]<ref name="Electron"/>
| {{SubatomicParticle|link=yes|Electron}}/{{SubatomicParticle|link=yes|Positron}}
| −1/+1
| {{frac|1|2}}
| +1/−1
| 0
| 0
| {{val|0.510998910|(13)}}
| Stable
| Stable
|-
|style="text-align:left"| [[Muon]] / [[Antimuon]]<ref name="Muon"/>
| {{SubatomicParticle|link=yes|Muon}}/{{SubatomicParticle|link=yes|Antimuon}}
| −1/+1
| {{frac|1|2}}
| 0
| +1/−1
| 0
| {{val|105.6583668|(38)}}
| {{val|2.197019|(21)|e=-6}}
| {{SubatomicParticle|link=yes|electron-}} + {{SubatomicParticle|link=yes|electron antineutrino}} + {{SubatomicParticle|link=yes|muon neutrino}}
|-
|style="text-align:left"| [[Tau (particle)|Tau]] / [[Antitau]]<ref name="Tauon"/>
| {{SubatomicParticle|link=yes|Tau}}/{{SubatomicParticle|link=yes|Antitau}}
| −1/+1
| {{frac|1|2}}
| 0
| 0
| +1/−1
| {{val|1776.84|(17)}}
| {{val|2.906|(10)|e=-13}}
| [http://pdg.lbl.gov/2008/listings/s035.pdf See {{SubatomicParticle|tau-}} decay modes]
|-
|style="text-align:left"| [[Electron neutrino]] / [[Electron antineutrino]]<ref name="Neutrino">C.Amsler et al. (2008): [http://pdg.lbl.gov/2008/listings/s066.pdf Particle listings – Neutrino properties]</ref>
| {{SubatomicParticle|link=yes|Electron neutrino}}/{{SubatomicParticle|link=yes|Electron antineutrino}}
| 0
| {{frac|1|2}}
| +1/−1
| 0
| 0
| < {{val|0.0000022}}<ref name="neutrinomass">J. Peltoniemi, J. Sarkamo (2005)</ref>
| Unknown
|
|-
|style="text-align:left"| [[Muon neutrino]] / [[Muon antineutrino]]<ref name="Neutrino"/>
| {{SubatomicParticle|link=yes|Muon neutrino}}/{{SubatomicParticle|link=yes|Muon antineutrino}}
| 0
| {{frac|1|2}}
| 0
| +1/−1
| 0
| < 0.17<ref name="neutrinomass" />
| Unknown
|
|-
|style="text-align:left"| [[Tau neutrino]] / [[Tau antineutrino]]<ref name="Neutrino"/>
| {{SubatomicParticle|link=yes|Tau neutrino}}/{{SubatomicParticle|link=yes|Tau antineutrino}}
| 0
| {{frac|1|2}}
| 0
| 0
| +1/−1
| < 15.5<ref name="neutrinomass" />
| Unknown
|
|}
 
== See also ==
{{Wikipedia books
|1=Leptons
|3=Particles of the Standard Model
}}
* [[Koide formula]]
* [[List of particles]]
* [[Quark]]
* [[Preon]]s – Hypothetical particles which were once postulated to be subcomponents of quarks and leptons
 
== Notes ==
{{Reflist|2}}
 
== References ==
*{{cite journal
|author=C. Amsler ''et al''. ([[Particle Data Group]])
|year=2008
|title=Review of Particle Physics
|journal=[[Physics Letters B]]
|volume=667 |page=1
|doi=10.1016/j.physletb.2008.07.018|bibcode = 2008PhLB..667....1P }}
*{{cite journal
|author=I.V. Anicin
|year=2005
|title=The Neutrino – Its Past, Present and Future
|journal=SFIN (Institute of Physics, Belgrade) year XV, Series A:  Conferences, No. A2 (2002) 3–59
|arxiv=physics/0503172
|bibcode = 2005physics...3172A
|pages=3172 }}
*{{cite journal
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|title=Evidence for Oscillation of Atmospheric Neutrinos
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|bibcode = 1998PhRvL..81.1562F }}
*{{cite journal
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|year=2001
|title=Observation of tau neutrino interactions
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*{{cite book
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|year=1992
|chapter=Chapter 2 – Leptons, quarks and hadrons
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|publisher=[[John Wiley & Sons]]
|isbn=0-471-92358-3
}}
*{{cite journal
|author=S.H. Neddermeyer, C.D. Anderson
|year=1937
|title=Note on the Nature of Cosmic-Ray Particles
|journal=[[Physical Review]]
|volume=51
|issue=10 |pages=884–886
|doi=10.1103/PhysRev.51.884
|bibcode = 1937PhRv...51..884N }}
*{{cite web
|author=J. Peltoniemi, J. Sarkamo
|year=2005
|url=http://cupp.oulu.fi/neutrino/nd-mass.html
|title=Laboratory measurements and limits for neutrino properties
|work=[http://cupp.oulu.fi/neutrino/ The Ultimate Neutrino Page]
|accessdate=2008-11-07
}}
*{{cite journal
|author=M.L. Perl ''et al''.
|year=1975
|title=Evidence for Anomalous Lepton Production in e<sup>+</sup>–e<sup>−</sup> Annihilation
|journal=[[Physical Review Letters]]
|volume=35 |issue=22 |pages=1489–1492
|doi=10.1103/PhysRevLett.35.1489
|bibcode = 1975PhRvL..35.1489P
|last2=Abrams
|first2=G.
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|last8=Dakin
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*{{cite book
|author=M.E. Peskin, D.V. Schroeder
|title=Introduction to Quantum Field Theory
|year=1995
|publisher=[[Westview Press]]
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*{{cite journal
|author=K. Riesselmann
|year=2007
|title=Logbook: Neutrino Invention
|url=http://www.symmetrymagazine.org/cms/?pid=1000450
|journal=[[Symmetry Magazine]]
|volume=4 |issue=2
}}
*{{cite book
|author=L. Rosenfeld
|year=1948
|title=Nuclear Forces
|page=xvii
|publisher=[[Interscience Publishers]]
}}
*{{cite book
|author=R. Shankar
|year=1994 |edition=2nd
|chapter=Chapter 2 – Rotational Invariance and  Angular Momentum
|title=Principles of Quantum Mechanics
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*{{cite book
|author=S. Weinberg
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*{{cite book
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== External links ==
{{Commons category|Leptons}}
{{wiktionary|lepton}}
*[http://pdg.lbl.gov Particle Data Group homepage]. The PDG compiles authoritative information on particle properties.
*[http://hyperphysics.phy-astr.gsu.edu/hbase/particles/lepton.html Leptons], a summary of leptons from ''[[Hyperphysics]]''.
 
{{particles}}
 
[[Category:Leptons| ]]
[[Category:Concepts in physics]]

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